1. Field of the Invention
The present invention relates to a high-efficiency expression technique of data by reducing redundancy, and a processing technique using this data.
2. Description of the Related Art
In recent years, non-linear dimension compression methods represented by “Isomap” of article 1 and “Locally Linear Embedding (LLE)” of article 2 have been proposed. Each of these methods provides a method of mapping data, which are considered to be present on a lower-dimensional manifold, onto a new low-dimensional space, which preserves the surface shape unique to the manifold to have an allowable level, on a high-dimensional space.
Such method is successful in highly efficient pattern expression in terms of expressing data by a lower-dimensional space. However, the method does not use information indicating classes to which data belong, and is not optimal to efficiently express data classifications.
By contrast, a method disclosed in Japanese Patent Laid Open No. 2005-535017 provides a method of expressing images for pattern classifications by extending the conventional Isomap method using a Kernel Fisher linear discriminant function or Fisher linear discriminant function.
Article 3 proposes, as the modification of the conventional Isomap method, a method of building a mapping relationship that enhances the separation degree by forcibly increasing the geodesic distance between data which belong to different classes.
In this way, a method which can preserve the surface shape unique to the manifold to have an allowable level, and can express data for pattern classifications is demanded.    [Article 1] Joshua B. Tenenbaum, Vin de Silva, John C. Langford, “A Global Geometric Framework for Nonlinear Dimensionality Reduction”, Science, Vol. 290, pp. 2319-2323, 2000    [Article 2] Sam T. Roweis, Lawrence K. Saul, “Nonlinear Dimensionality Reduction by Locally Linear Embedding”, Science, Vol. 290, pp. 2323-2326, 2000    [Article 3] Bisser Raytchev, Ikushi Yoda, Katsuhiko Sakaue, “Multi-View Face Recognition By Nonlinear Dimensionality Reduction And Generalized Linear Models”, Proceedings of the 7th International Conference on Automatic Face Gesture Recognition, pp. 625-630, 2006